A034789 Related to sextic factorial numbers A008542.

1, 21, 546, 15561, 466830, 14471730, 458960580, 14801478705, 483514971030, 15955994043990, 530899438190940, 17785131179396490, 599222112044281740, 20287948650642110340, 689790254121831751560, 23539092421907508521985

Offset

1,2

Comments

Convolution of A004993(n-1) with A025751(n), n >= 1.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..645

Elżbieta Liszewska, Wojciech Młotkowski, Some relatives of the Catalan sequence, arXiv:1907.10725 [math.CO], 2019.

Formula

a(n) = 6^(n-1)*A008542(n)/n!.

G.f.: (-1+(1-36*x)^(-1/6))/6.

D-finite with recurrence: n*a(n) +6*(-6*n+5)*a(n-1)=0. - R. J. Mathar, Jan 28 2020

Maple

seq( 6^(n-1)*mul(6*j-5, j=1..n)/n!, n=1..20); # G. C. Greubel, Nov 11 2019

Mathematica

Rest@ CoefficientList[Series[(-1 + (1 - 36 x)^(-1/6))/6, {x, 0, 16}], x] (* Michael De Vlieger, Oct 13 2019 *)
Table[6^(2*n-1)*Pochhammer[1/6, n]/n!, {n, 20}] (* G. C. Greubel, Nov 11 2019 *)

Prog

(PARI) vector(20, n, 6^(n-1)*prod(j=1, n, 6*j-5)/n! ) \\ G. C. Greubel, Nov 11 2019
(Magma) [6^(n-1)*(&*[6*j-5: j in [1..n]])/Factorial(n): n in [1..20]]; // G. C. Greubel, Nov 11 2019
(Sage) [6^(n-1)*product( (6*j-5) for j in (1..n))/factorial(n) for n in (1..20)] # G. C. Greubel, Nov 11 2019
(GAP) List([1..20], n-> 6^(n-1)*Product([1..n], j-> 6*j-5)/Factorial(n) ); # G. C. Greubel, Nov 11 2019

Crossrefs

Cf. A008542, A034687.

Sequence in context: A221766 A080483 A015255 * A297635 A292062 A194022

Adjacent sequences: A034786 A034787 A034788 * A034790 A034791 A034792

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved